Most Cited Fuzzy Sets and Systems Articles
The most cited articles published since 2011, extracted from Scopus.
Gradualness, uncertainty and bipolarity: Making sense of fuzzy setsDidier Dubois | Henri Prade
Volume 192, Issue , April 2012, Pages 3-24
This paper discusses basic notions underlying fuzzy sets, especially gradualness, uncertainty, vagueness and bipolarity, in order to clarify the significance of using fuzzy sets in practice. Starting with the idea that a fuzzy set may represent either a precise gradual composite entity or an epistemic construction refereeing to an ill-known object, it is shown that each of this view suggests a different use of fuzzy sets. Then, it is argued that the usual phrase fuzzy number is ambiguous as it induces some confusion between gradual extensions of real numbers and gradual extensions of interval calculations. The distinction between degrees of truth that are compositional and degrees of belief that cannot be so is recalled. The truth-functional calculi of various extensions of fuzzy sets, motivated by the desire to handle ill-known membership grades, are shown to be of limited significance for handling this kind of uncertainty. Finally, the idea of a separate handling of membership and non-membership grades put forward by Atanassov is cast in the setting of reasoning about bipolar information. This intuition is different from the representation of ill-known membership functions and leads to combination rules differing from the ones proposed for handling uncertainty about membership grades. © 2010 Elsevier B.V. All rights reserved.
Observer-based adaptive fuzzy tracking control for a class of uncertain nonlinear MIMO systemsYan Jun Liu | Shao Cheng Tong | Tie Shan Li
Volume 164, Issue 1, February 2011, Pages 25-44
This paper addresses the adaptive fuzzy tracking control problem for a class of uncertain nonlinear MIMO systems with the external disturbances. The adaptive fuzzy controllers are designed under the constraint that only system output is available for measurement. Then, it is needed to design a state observer to estimate the unmeasured states. In the observer design procedure, two prominent advantages are that it does not require the sign of the control gain coefficient to be known and only two parameters need to be adjusted on-line for each subsystem. By using Lyapunov analysis method, it is proven that all the signals in the closed-loop system are guaranteed to be bounded and the system outputs track the reference signals to a bounded compact set. The feasibility of the proposed approach is validated by using two simulation examples. © 2010 Elsevier B.V. All rights reserved.
Adaptive fuzzy terminal sliding mode control for a class of MIMO uncertain nonlinear systemsV. Nekoukar | A. Erfanian
Volume 179, Issue 1, September 2011, Pages 34-49
This paper presents a new adaptive terminal sliding mode tracking control design for a class of nonlinear systems using fuzzy logic system. The terminal sliding mode control (TSM) was developed to provide faster convergence and higher-precision control than the linear hyperplane-based sliding control. However, the original TSM encountered singularity problem with discontinuous control action. Moreover, a prior knowledge about the plant to be controlled is required. The proposed controller combines a continuous non-singular TSM with an adaptive learning algorithm and fuzzy logic system to estimate the dynamics of the controlled plant so that closed-loop stability and finite-time convergence of tracking errors can be guaranteed. The performance of the proposed control strategy is evaluated through the control of a two-link rigid robotic manipulator. Finally, the effectiveness of the proposed scheme is demonstrated through the control of the ankle and knee movements in paraplegic subjects using functional electrical stimulation. Simulation and experimental results verify that the proposed control strategy can achieve favorable control performance with regard to system parameter variations and external disturbances. © 2011 Elsevier B.V. All rights reserved.
Continuous generalized OWA operator and its application to decision makingLi Gang Zhou | Hua You Chen
Volume 168, Issue 1, April 2011, Pages 18-34
In this paper we present a new class of operators called the continuous generalized ordered weighted averaging (C-GOWA) operators, which extends the continuous ordered weighted averaging operator. To adapt to uncertain and complex situations in decision making, we use differentiated aggregation method and produce special forms of C-GOWA operator. In addition, we apply the C-GOWA operator to the aggregation of multiple interval arguments and obtain a wide range of aggregation operators. We especially discuss the controlling parameter and the selection of basic unit-interval monotonic function, introduced in the information aggregation, to make it more feasible. We further generalize the previous approaches by using Choquet integral and quasi-arithmetic means, obtaining the combined continuous generalized Choquet integral aggregation operator and the combined continuous quasi-arithmetic Choquet integral aggregation operator. We also present some further extension by using hierarchical aggregation rules, obtaining the ordered hierarchies of the combined C-GOWA operator. Meanwhile, some desirable properties of these operators are investigated. Finally, we give a numerical example to illustrate the application of these operators to group decision making with interval arguments. © 2010 Elsevier B.V.
The role of fuzzy sets in decision sciences: Old techniques and new directionsDidier Dubois
Volume 184, Issue 1, December 2011, Pages 3-28
We try to provide a tentative assessment of the role of fuzzy sets in decision analysis. We discuss membership functions, aggregation operations, linguistic variables, fuzzy intervals and the valued preference relations they induce. The importance of the notion of bipolarity and the potential of qualitative evaluation methods are also pointed out. We take a critical standpoint on the state-of-the-art, in order to highlight the actual achievements and question what is often considered debatable by decision scientists observing the fuzzy decision analysis literature. © 2011 Elsevier B.V. All rights reserved.
Adaptive fuzzy controller for multivariable nonlinear state time-varying delay systems subject to input nonlinearitiesA. Boulkroune | M. M'Saad | M. Farza
Volume 164, Issue 1, February 2011, Pages 45-65
In this paper, an adaptive fuzzy variable-structure controller is investigated for a class of uncertain multi-input multi-output (MIMO) nonlinear time-delay systems with both sector nonlinearities and dead-zones. A decomposition property of the control-gain matrix is fully exploited in the controller design and the stability analysis. The unknown time-varying delay uncertainties are compensated for using an appropriate Lyapunov-Krasovskii functional. The boundedness of all signals of the closed-loop system as well as the exponential convergence of the underlying tracking errors to an adjustable region are established. The effectiveness of the proposed fuzzy adaptive controller is illustrated throughout simulation results. © 2010 Elsevier B.V. All rights reserved.
Variation of constant formula for first order fuzzy differential equationsA. Khastan | J. J. Nieto | Rosana Rodríguez-López
Volume 177, Issue 1, August 2011, Pages 20-33
In this paper, we study first order linear fuzzy differential equations by using the generalized differentiability concept and we present the general form of their solutions. We also correct and complete some previous results. Finally, some examples are given to illustrate our results. © 2011 Elsevier B.V. All rights reserved.
Generation of linear orders for intervals by means of aggregation functionsH. Bustince | J. Fernandez | A. Kolesárová | R. Mesiar
Volume 220, Issue , June 2013, Pages 69-77
The problem of choosing an appropriate total order is crucial for many applications that make use of extensions of fuzzy sets. In this work we introduce the concept of an admissible order as a total order that extends the usual partial order between intervals. We propose a method to build these admissible orders in terms of two aggregation functions and we prove that some of the most used examples of total orders that appear in the literature are specific cases of our construction. © 2012 Elsevier B.V.
Generalized differentiability of fuzzy-valued functionsBarnabás Bede | Luciano Stefanini
Volume 230, Issue , November 2013, Pages 119-141
In the present paper, using novel generalizations of the Hukuhara difference for fuzzy sets, we introduce and study new generalized differentiability concepts for fuzzy valued functions. Several properties of the new concepts are investigated and they are compared to similar fuzzy differentiabilities finding connections between them. Characterization and relatively simple expressions are provided for the new derivatives. © 2012 Elsevier B.V. All rights reserved.
Robust possibilistic programming for socially responsible supply chain network design: A new approachM. S. Pishvaee | J. Razmi | S. A. Torabi
Volume 206, Issue , November 2012, Pages 1-20
The importance of social responsibility of corporate and business units is increasingly emphasized by researchers and practitioners in recent years. Since supply chains play important roles in todays business environment, the issue of social responsibility should be considered carefully when designing and planning of supply chains to move towards sustainability. This paper addresses the problem of socially responsible supply chain network design under uncertain conditions. To this aim, first a bi-objective mathematical programming model is developed wherein its objective functions include minimizing the total cost and maximizing the supply chain social responsibility. Then, for coping with uncertain parameters effectively, a novel possibilistic programming approach, called robust possibilistic programming (RPP), is proposed. Several varieties of RPP models are developed and their differences, weaknesses, strengths and the most suitable conditions for being used are discussed. A real industrial case study is provided to illustrate the performance and applicability of the proposed RPP models in practice. © 2012 Elsevier B.V.
Least square completion and inconsistency repair methods for additively consistent fuzzy preference relationsXinwang Liu | Yuwen Pan | Yejun Xu | Shui Yu
Volume 198, Issue , July 2012, Pages 1-19
In this paper, we explore the group decision making (GDM) problems with incomplete additively consistent fuzzy preference relations. Some properties of additively consistent fuzzy preference relations are also discussed. A sufficient and necessary condition is proposed to keep the additive consistency of fuzzy preference relations. Methods for determining the priority weights of fuzzy preference relations are provided. Least square completion and inconsistency repair methods are developed to deal with incomplete and inconsistent fuzzy preference relations. Some numerical examples are also given to illustrate the proposed approaches. © 2011 Elsevier B.V.
Polynomial-based radial basis function neural networks (P-RBF NNs) realized with the aid of particle swarm optimizationSung Kwun Oh | Wook Dong Kim | Witold Pedrycz | Byoung Jun Park
Volume 163, Issue 1, January 2011, Pages 54-77
In this study, we design polynomial-based radial basis function neural networks (P-RBF NNs) based on a fuzzy inference mechanism. The essential design parameters (including learning rate, momentum coefficient and fuzzification coefficient of the underlying clustering method) are optimized by means of the particle swarm optimization. The proposed P-RBF NNs dwell upon structural findings about training data that are expressed in terms of a partition matrix resulting from fuzzy clustering in this case being the fuzzy C-means (FCM). The network is of functional nature as the weights between the hidden layer and the output are some polynomials. The use of the polynomial weights becomes essential in capturing the nonlinear nature of data encountered in regression or classification problems. From the perspective of linguistic interpretation, the proposed network can be expressed as a collection of "if-then" fuzzy rules. The architecture of the networks discussed here embraces three functional modules reflecting the three phases of input-output mapping realized in rule-based architectures, namely condition formation, conclusion creation, and aggregation. The proposed classifier is applied to some synthetic and machine learning datasets, and its results are compared with those reported in the previous studies. © 2010 Elsevier B.V. All rights reserved.
An improved result on the stability of uncertain T-S fuzzy systems with interval time-varying delayChen Peng | Min Rui Fei
Volume 212, Issue , February 2013, Pages 97-109
This paper is concerned with the stability of uncertain T-S fuzzy systems with interval time-varying delay. By uniformly dividing the delay interval into multiple segments and constructing an appropriate augmented Lyapunov-Krasovskii functional, some less conservative stability criteria are obtained, which include some existing results as special cases. Since a tighter bounding inequality is employed to deal with time-varying delay-dependent integral items, then some sources of computational complexity, such as the general convex combination and free weighting matrices are not necessary to be adopted in the derivation of our results. As a result, the developed criteria not only theoretically improve some existing results, but also have higher computational efficiency. Numerical examples are given to demonstrate the effectiveness of the proposed method. © 2012 Elsevier B.V.
Universal fuzzy controllers based on generalized T-S fuzzy modelsQing Gao | Gang Feng | Yong Wang | Jianbin Qiu
Volume 201, Issue , August 2012, Pages 55-70
This paper investigates the universal fuzzy control problem based on generalized T-S fuzzy models. The universal approximation capability of the generalized T-S fuzzy models is shown and an approach to robust controller design for general nonlinear systems based on this kind of generalized T-S fuzzy models is developed. The results of universal fuzzy controllers for two classes of nonlinear systems are then given, and constructive procedures to obtain the universal fuzzy controllers are also provided. An example is finally presented to show the effectiveness of our approach. © 2012 Elsevier B.V. All rights reserved.
Non-quadratic local stabilization for continuous-time Takagi-Sugeno modelsThierry Marie Guerra | Miguel Bernal | Kevin Guelton | Salim Labiod
Volume 201, Issue , August 2012, Pages 40-54
This paper is concerned with non-quadratic stabilization of continuous-time Takagi-Sugeno (TS) models. The well-known problem of handling time-derivatives of membership functions (MFs) as to obtain conditions in the form of linear matrix inequalities (LMIs) is overcome by reducing global goals to the estimation of a region of attraction. Instead of parallel distributed compensation (PDC), a non-PDC control law is proposed according to the non-quadratic nature of the Lyapunov function. Examples are provided to show the advantages over the quadratic and some non-quadratic approaches. © 2011 Elsevier B.V. All rights reserved.
Sampled-data robust H ∞ control for T-S fuzzy systems with time delay and uncertaintiesChen Peng | Qing Long Han | Dong Yue | Engang Tian
Volume 179, Issue 1, September 2011, Pages 20-33
This paper investigates sampled-data robust H∞ control for T-S fuzzy systems with time delay and uncertainties. By introducing the free weighting matrices to deal with the integral items and converting the coupling time-varying matrix inequalities into a group of decoupling matrix inequalities, an innovative delay-dependent stabilization criterion is first presented. Then, a sampled-data H∞ controller is designed to stabilize the T-S fuzzy system to achieve the prescribed disturbance attenuation level, which is dependent on both the size of state delay and upper bound of allowable sampling period. Since (1) the sawtooth structure of delay is fully considered; (2) neither model transformation nor bounding techniques are employed in deriving the delay-dependent results; and (3) none of the integral items are arbitrarily ignored and magnified, the less conservative results can be expected. A practical application example is given to demonstrate the effectiveness of the proposed methods. © 2011 Elsevier B.V. All rights reserved.
Citation-based journal ranks: The use of fuzzy measuresGleb Beliakov | Simon James
Volume 167, Issue 1, March 2011, Pages 101-119
This article considers a real-world application of the Choquet integral-based classifier to the problem of ranking of scientific journals. We attempted to predict rankings given by panels of experts, by using available citation indices. We compare the Choquet integral fit by the least absolute deviation criterion as a classifier against other ordinal classification methods, before interpreting the fuzzy measure weights and indices. Our findings show that the journal rankings data set is difficult to model accurately due to inconsistencies and lack of monotonicity, but that the Choquet integral still performs well as a classifier. © 2010 Elsevier B.V.
On-line incremental feature weighting in evolving fuzzy classifiersEdwin Lughofer
Volume 163, Issue 1, January 2011, Pages 1-23
In this paper, we present an approach for addressing the problem of dynamic dimension reduction during on-line training, evolution and updating of evolving fuzzy classifiers (EFC). The basic idea of our approach is that, instead of permanently changing the list of most important features with newly loaded data blocks, we generalize the concept of incremental feature selection to an incremental feature weighting approach: features are assigned weights in [0,1] according to their importance level. These weights are permanently updated during on-line mode and guarantee a smooth learning process in the evolving fuzzy classifiers, as they change softly and continuously over time. In some cases, when the weights become (approximately) 0, an automatic switching off of some features and therefore a (soft) dimension reduction is achieved. Two novel incremental feature weighting strategies are proposed in this paper, one based on a leave-one-feature-out, the other based on a feature-wise separability criterion. We will describe the integration concept of the feature weights in the evolving fuzzy classifiers, using single and multi-model architecture, where FLEXFIS-Class SM and FLEXFIS-Class MM serve as training engines. The whole approach of integrated incremental feature weighting in evolving fuzzy classifiers will be evaluated based on high-dimensional on-line real-world classification scenarios and based on data from the Internet. The results will show that incremental feature weighting in EFC in fact helps to reduce curse of dimensionality and therefore guides the evolving fuzzy classifiers to a higher on-line predictive power. © 2010 Elsevier B.V. All rights reserved.
Maximum likelihood estimation from fuzzy data using the em algorithmThierry Denœux
Volume 183, Issue 1, November 2011, Pages 72-91
A method is proposed for estimating the parameters in a parametric statistical model when the observations are fuzzy and are assumed to be related to underlying crisp realizations of a random sample. This method is based on maximizing the observed-data likelihood defined as the probability of the fuzzy data. It is shown that the EM algorithm may be used for that purpose, which makes it possible to solve a wide range of statistical problems involving fuzzy data. This approach, called the fuzzy EM (FEM) method, is illustrated using three classical problems: normal mean and variance estimation from a fuzzy sample, multiple linear regression with crisp inputs and fuzzy outputs, and univariate finite normal mixture estimation from fuzzy data. © 2011 Elsevier B.V. All rights reserved.
Exponential and almost sure exponential stability of stochastic fuzzy delayed Cohen-Grossberg neural networksQuanxin Zhu | Xiaodi Li
Volume 203, Issue , September 2012, Pages 74-94
In this paper, we study a class of stochastic fuzzy delayed Cohen-Grossberg neural networks. Two kinds of stability are discussed in our investigation. One is exponential stability in the mean square and the other is almost sure exponential stability. First, some sufficient conditions are derived to guarantee the exponential stability in the mean square for the considered system based on the Lyapunov-Krasovskii functional, stochastic analysis theory and the Itô's formula as well as the Dynkin formula. Then, we further investigate the almost sure exponential stability by employing the nonnegative semi-martingale convergence theorem. Moreover, we prove that the addressed system is both almost sure exponentially stable and exponentially stable in the mean square under suitable conditions. Finally, three numerical examples are also given to show the effectiveness of the theoretical results. In particular, the simulation figures establish that fuzzy systems do have more advantages than non-fuzzy systems. © 2012 Elsevier B.V. All rights reserved.
The law of importation versus the exchange principle on fuzzy implicationsSebastia Massanet | Joan Torrens
Volume 168, Issue 1, April 2011, Pages 47-69
Some open problems on fuzzy implications dealing with the so-called importation law are studied and totally or partially solved in this work. A weaker version of the law of importation, called the weak law of importation, is introduced. The relationships of these two properties and the exchange principle are studied. In particular, it is proved that the law of importation is stronger than the exchange principle. On the other hand, the three properties are equivalent for some kind of fuzzy implications, those that satisfy a boundary property. Along this study, new characterizations of (S,N)-implications, R-implications and their counterparts for uninorms based on the weak law of importation are showed. © 2010 Elsevier B.V.
A single-point characterization of representable uninormsJános Fodor | Bernard De Baets
Volume 202, Issue , September 2012, Pages 89-99
We study uninorms of which both the underlying t-norm and underlying t-conorm are strict. Such uninorms are the only candidates for being representable by an additive generator. We prove that the representability of such a uninorm depends solely on its value at a single arbitrary point in the 'remaining' open part of the unit square. More explicitly, such a uninorm turns out to be representable if and only if this single value is located strictly between the minimum and the maximum of the corresponding arguments. If this single value coincides with one of these bounds, then the value of the uninorm at any point in the 'remaining' open part is determined by the same bound. © 2011 Published by Elsevier B.V.
On the failure of the finite model property in some Fuzzy Description LogicsFernando Bobillo | Félix Bou | Umberto Straccia
Volume 172, Issue 1, June 2011, Pages 1-12
Fuzzy Description Logics (DLs) are a family of logics which allow the representation of (and the reasoning with) structured knowledge affected by vagueness. Although most of the not very expressive crisp DLs, such as ALC, enjoy the Finite Model Property (FMP), this is not the case once we move into the fuzzy case. In this paper we show that if we allow arbitrary knowledge bases, then the fuzzy DLs ALC under Łukasiewicz and Product fuzzy logics do not verify the FMP even if we restrict to witnessed models; in other words, finite satisfiability and witnessed satisfiability are different for arbitrary knowledge bases. The aim of this paper is to point out the failure of FMP because it affects several algorithms published in the literature for reasoning under fuzzy DLs. © 2011 Elsevier B.V. All rights reserved.
The Choquet integral with respect to a level dependent capacitySalvatore Greco | Benedetto Matarazzo | Silvio Giove
Volume 175, Issue 1, July 2011, Pages 1-35
We present a generalization of Choquet integral in which the capacity depends also on the value of the aggregated variables. We show that as particular cases of our generalization of Choquet integral there are the Sugeno integral, the Šipoš integral and the Cumulative Prospect Theory functional. We also show that many concepts such as Möbius transform, importance index, interaction index, k-order capacities and OWA operators, introduced in the research about Choquet integral, can be generalized in the considered context. © 2011 Elsevier B.V. All Rights Reserved.
On set-valued stochastic integrals and fuzzy stochastic equationsMariusz Michta
Volume 177, Issue 1, August 2011, Pages 1-19
In this paper we extend the notion of set-valued and fuzzy stochastic integrals to semimartingale integrators. We present their main properties and finally we establish the existence of solutions of a fuzzy integral stochastic equation driven by a Brownian motion. The approach is based on the existence of solutions of an appropriately formulated martingale problem for a system of stochastic inclusions and the theorem of Negoita and Ralescu. © 2011 Elsevier B.V. All rights reserved.